By Muneo Hori

Computational mechanics has made a powerful influence on classical continuum mechanics, such as engineering mechanics and constitution mechanics. Earthquake engineering has completed major development by means of computational mechanics. This publication covers a few new facets of earthquake engineering which are in response to computational mechanics, i.e., computational earthquake engineering.

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**Extra resources for Introduction to Computational Earthquake Engineering**

**Example text**

The first variation of I is 61= 8cTi(cri/c- X,i)dsx+ JB IB / rii6(7i{X JdB JdB -u°)dtx. Hence, it is required that strain given by <7j/c is 7 compatible, and A coincides with 6 T h e spatial integration and the probabilistic integration are commuted in deriving Eq. 7). C o m p a t i b i l i t y of strain means that strain must be associated with displacement. In the present case, u generates strain [ e i , e 2 ] T = [ « , i , « , 2 ] T (ti=2t3i)- For [ c i , ^ ] 7 * to be related to one function Stochastic Modeling 39 the exact displacement u e x a c t .

This is spectral stochastic finite element method (SSFEM). When {um} are obtained, the joint probability between c(u>) and u(ui) can be computed since they are expanded in {£ n (w)} and {* m (ui)}. It should be mentioned that SSFEM is different from an ordinary stochastic finite element method (SFEM) which takes perturbation for stochastic parameters assuming that they are smaller than deterministic parts; see [Hisada and Nakagiri (1981)], [Yamazaki and Shinozuka (1988)] and [Der Kiureghian and Ke (1988)].

1 Introduction to Computational Earthquake Engineering Basics of the Wave Equation As the simplest problem of wave propagation phenomenon, a one dimensional problem of an elastic rod is considered. Young's modulus and density of the rod are E and p, respectively, and the cross section area is 1. , e(x,t) = u'(x,t), a'(x,t) - pu{x,t), a(x,t) = Ee(x,t). 1) Here, u, e and a are displacement, strain and stress which are functions of place and time, x and t, and prime and dot stand for derivative with respect to x and t, respectively.